Finite Group Databasebeta

?

← Prev (#7707871) Next (#7707873) →

C₂×#51940 #7707872

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

9134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

(1,2);(3,4)(5,6)(7,8)(9,10)(19,20)(21,25)(22,26)(23,24);(4,8)(5,9)(11,12,14,15)(13,17,18,16)(19,21)(20,22)(23,26)(24,25);(12,15)(16,17)(20,24)(21,26);(3,5,7,9)(4,6,8,10)(11,12)(13,16)(14,15)(17,18)(19,21)(20,25)(22,24)(23,26);(3,6)(4,9)(5,8)(7,10)(11,13,14,18)(12,16,15,17)(19,22,23,25)(20,21,24,26)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7615068);